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A. Y. Kitaev, Quantum computations: algorithms and error correction, Russian Mathematical Surveys 52
1997
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary (1998), arXiv:quant-ph/9811052 [quant-ph]
1998
Earlier work this paper cites.
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics 43
2002
Earlier work this paper cites.
A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of physics 303
2003
Earlier work this paper cites.
S. Bravyi, M. B. Hastings, and F. Verstraete, Lieb-Robinson bounds and the generation of correlations and topological quantum order, Physical Review Letters 97
2006
Earlier work this paper cites.
G. Vidal, Class of quantum many-body states that can be efficiently simulated, Physical Review Letters 101
2008
Earlier work this paper cites.

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M. Aguado and G. Vidal, Entanglement renormalization and topological order, Physical Review Letters 100
2008
Cited alongside, same era.
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Physical Review A 86
2012
Cited alongside, same era.
P. Liao and D. L. Feder, Graph-state representation of the toric code, Physical Review A 104
2021
Cited alongside, same era.
O. Higgott, M. Wilson, J. Hefford, J. Dborin, F. Hanif, S. Burton, and D. E. Browne, Optimal local unitary encoding circuits for the surface code, Quantum 5
2021
Cited alongside, same era.
C. Gidney, N. Shutty, and C. Jones, Magic state cultivation: Growing T states as cheap as CNOT gates (2024), arXiv:2409.17595 [quant-ph]
Original
2024
Cited alongside, same era.

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2025

Lower-depth local encoding circuits for the surface code

Claes, Jahan

Understand

The surface code is the most studied error-correcting code thanks to its high threshold, simple decoding, and locality in two dimensions (2D).

A key component of any code is its encoding circuit, which maps an unencoded state to the corresponding encoded state.
The best previous surface code encoding circuit compatible with 2D local connectivity requires depth $2d$ to encode distance-$d$ surface codes.
This paper presents depth $d$ encoding circuits for the rotated surface code.

Built on

A. Y. Kitaev, Quantum computations: algorithms and error correction, Russian Mathematical Surveys 52
1997
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary (1998), arXiv:quant-ph/9811052 [quant-ph]
1998
Earlier work this paper cites.
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics 43
2002
Earlier work this paper cites.
A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of physics 303
2003
Earlier work this paper cites.
S. Bravyi, M. B. Hastings, and F. Verstraete, Lieb-Robinson bounds and the generation of correlations and topological quantum order, Physical Review Letters 97
2006
Earlier work this paper cites.
G. Vidal, Class of quantum many-body states that can be efficiently simulated, Physical Review Letters 101
2008
Earlier work this paper cites.

Similar

M. Aguado and G. Vidal, Entanglement renormalization and topological order, Physical Review Letters 100
2008
Cited alongside, same era.
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Physical Review A 86
2012
Cited alongside, same era.
P. Liao and D. L. Feder, Graph-state representation of the toric code, Physical Review A 104
2021
Cited alongside, same era.
O. Higgott, M. Wilson, J. Hefford, J. Dborin, F. Hanif, S. Burton, and D. E. Browne, Optimal local unitary encoding circuits for the surface code, Quantum 5
2021
Cited alongside, same era.
C. Gidney, N. Shutty, and C. Jones, Magic state cultivation: Growing T states as cheap as CNOT gates (2024), arXiv:2409.17595 [quant-ph]
Original
2024
Cited alongside, same era.

Then

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alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature 626

2024

Cited alongside, same era.

P. S. Rodriguez, J. M. Robinson, P. N. Jepsen, Z. He, C. Duckering, C. Zhao, K.-H. Wu, J. Campo, K. Bagnall, M. Kwon, T. Karolyshyn, P. Weinberg, M. Cain, S. J. Evered, A. A. Geim, M. Kalinowski, S. H. Li, T. Manovitz, J. Amato-Grill, J. I. Basham, L. Bernstein, B. Braverman, A. Bylinskii, A. Choukri, R. DeAngelo, F. Fang, C. Fieweger, P. Frederick, D. Haines, M. Hamdan, J. Hammett, N. Hsu, M.-G. Hu, F. Huber, N. Jia, D. Kedar, M. Kornjača, F. Liu, J. Long, J. Lopatin, P. L. S. Lopes, X.-Z. Luo, T. Macrì, O. Marković, L. A. Martínez-Martínez, X. Meng, S. Ostermann, E. Ostroumov, D. Paquette, Z. Qiang, V. Shofman, A. Singh, M. Singh, N. Sinha, H. Thoreen, N. Wan, Y. Wang, D. Waxman-Lenz, T. Wong, J. Wurtz, A. Zhdanov, L. Zheng, M. Greiner, A. Keesling, N. Gemelke, V. Vuletić, T. Kitagawa, S.-T. Wang, D. Bluvstein, M. D. Lukin, A. Lukin, H. Zhou, and S. H. Cantú, Experimental demonstration of logical magic state distillation (2024a), arXiv:2412.15165 [quant-ph]

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P. S. Rodriguez, J. M. Robinson, P. N. Jepsen, Z. He, C. Duckering, C. Zhao, K. Wu, J. Campo, K. Bagnall, M. Kwon, et al. , Experimental demonstration of logical magic state distillation (2024b), arXiv:2412.15165

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K. J. Satzinger, Y. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, C. Gidney, I. Aleiner, F. Arute, K. Arya, J. Atalaya, R. Babbush, J. C. Bardin, R. Barends, J. Basso, A. Bengtsson, A. Bilmes, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. R. Derk, D. Eppens, C. Erickson, E. Farhi, L. Foaro, A. G. Fowler, B. Foxen, M. Giustina, A. Greene, J. A. Gross, M. P. Harrigan, S. D. Harrington, J. Hilton, S. Hong, T. Huang, W. J. Huggins, L. B. Ioffe, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, T. Khattar, S. Kim, P. V. Klimov, A. N. Korotkov, F. Kostritsa, D. Landhuis, P. Laptev, A. Locharla, E. Lucero, O. Martin, J. R. McClean, M. McEwen, K. C. Miao, M. Mohseni, S. Montazeri, W. Mruczkiewicz, J. Mutus, O. Naaman, M. Neeley, C. Neill, M. Y. Niu, T. E. O’Brien, A. Opremcak, B. Pató, A. Petukhov, N. C. Rubin, D. Sank, V. Shvarts, D. Strain, M. Szalay, B. Villalonga, T. C. White, Z. Yao, P. Yeh, J. Yoo, A. Zalcman, H. Neven, S. Boixo, A. Megrant, Y. Chen, J. Kelly, V. Smelyanskiy, A. Kitaev, M. Knap, F. Pollmann, and P. Roushan, Realizing topologically ordered states on a quantum processor, Science 374

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2025

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